Explain how to determine if the answer is positive or negative when evaluating an expression with an integer power and negative base such as \left( - 7 \right)^{3}.

Consider the expressions \left( - 3 \right)^{2} and - 3^{2}.

Explain how to evaluate - 3^{2}.

Explain how to evaluate (- 3)^2.

Write 4^{3} in expanded form.

Now, evaluate 4^{3}.

Write \left( -2 \right)^{5} in expanded form.

Now, evaluate \left( -2 \right)^{5}.

Evaluate:

3^{1}

1^{3}

2^{6}

- 6^{3}

\left( - 4 \right)^{3}

- 5^{3}

- 15^{2}

- \left( - 8 \right)^{2}

Evaluate:

5^{2} + 3^{3}

2^{2} + 4^{3}

7^{2} - 2^{2}

4^{3} - 2^{3}

12^{2} - 2^{2}

\left( - 2 \right)^{3} + 5^{2}

\left( - 11 \right)^{2} - \left( - 9 \right)^{2}

- \left( - 3 \right)^{3} + 8^{2}

Evaluate:

1 + \left(3 + 2\right)^{2}

\left(10 + 2 \right) - 2^{3}

4 - \left(5 - 2\right)^{2}

6 - \left(12 - 3^{2}\right)

9 - 2^{2} \times \left( - 7 \right)

\left(2 - 5\right)^{2} \times \left( - 21 + 14\right)

- \left( - 4 \right)^{3} - \left( - 10 \right)^{2} - 122

150 + 6^{2} - \left( - 10 + 8 \right)^{3}

Evaluate:

3^{3} \times 3^{2}

\left( - 9 \right) \times \left( - 6 \right)^{2}

\left( - 2 \right)^{3} \times 3^{4}

\left( - 3 \right)^{2} \times \left( - 2 \right)^{2}

\dfrac{3^{5}}{3^{3}}

\dfrac{4^{4}}{4^{2}}

\dfrac{(-2)^{4}}{(-2)^{3}}

\dfrac{(-5)^{5}}{5^{3}}

Ralph tried to evaluate the expression 2 \times \left(3+2\right)^2. He thought that he had the right answer and submitted the following to his teacher: \begin{aligned} 2 \times \left(3+2\right)^2 &= 2 \times \left(5\right)^2 \\ &= 10^2 \\ & = 100 \end{aligned}

State the error Ralph made.

Write the correct work and answer.

Outcomes

MA.7.NSO.1.1

Know and apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to whole-number exponents and rational number bases.

1.08 Evaluate expressions involving powers

Outcomes

MA.7.NSO.1.1

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